Sakya (Wyl. sa skya), which is one of the four main traditions of Tibetan Buddhism, takes its name from the Sakya Monastery, founded by Khön Könchok Gyalpo in 1073. The name Sakya literally means 'grey earth', and is a reference to the unusually pale colour of the earth at the site. Due to the widespread influence of the monastery's earliest masters, especially the so called 'Five Sakya Patriarchs', it quickly developed into one of the main schools in Tibet, developing a special reputation for scholarship. The most important teaching within the Sakya tradition is the Lamdré, or 'Path with Its Fruit', a series of meditation instructions associated with the Hevajra Tantra.

Sakya refers to the place name of the main monastery of the Khon family lineage in Tibet. Sakya means "grey earth". Other transliterations are also possible: Sa skya, I think in Hopkin's system he transliterates this to Sa ga.

Shakyamuni indeed means Sage (muni) of the Shakya clan. The Shakya clan was a clanal/tribal unit in north India. They were basically wiped out in a war during Shakyamuni Buddha's lifetime.

You are confusing coincidental transliterations from Tibetan and Sanskrit that just happen to have several phonemes in common.

Just for the record of the Sanskrit / Pali, Sanskrit "Śākya" or Pali "Sākya" is the name of the clan, "Śākyamuni" means the "sage" (muni) of the "Śākya [clan]". But in Sanskrit the distinction between "Shakya" and "Sakya" really only works in English, because in Pali both are just "S-", and in Sanskrit "Ś-". Some people - but not all - make Sanskrit "Ś" into English "Sh".

Just for the record of the Sanskrit / Pali, Sanskrit "Śākya" or Pali "Sākya" is the name of the clan, "Śākyamuni" means the "sage" (muni) of the "Śākya [clan]". But in Sanskrit the distinction between "Shakya" and "Sakya" really only works in English, because in Pali both are just "S-", and in Sanskrit "Ś-". Some people - but not all - make Sanskrit "Ś" into English "Sh".